Perhaps the UEF isn't as peaceful as suggested.
Let us remember that it was a coterie of psychohistorians and sociopsychologists who "predicted" the ideological armaggedon brought on about by a "radical" religious group that would eradicate away the GTVA's own
existence.
Consider two different scenarios. The first that this particular coterie of experts were actually
right in projecting the downfall of the current GTVA's political authority among its own population, and the eventual degradation and collapse of its structure. This is completely realistic: the "american dream" of freedom and wealth that has inspired a lot of revolutions around the world, and has brought about actual collapse of totalitarian regimes. It's something also called "Soft Power".
The second that this coterie of scientists were actually wrong, on either purely scientific reasons (missed key elements perhaps) or by fiat (scientific malfeasance to induce politics). In this scenario it wouldn't be impossible a joint effort by both the GTVA and the Sol planets to share their knowledge and technologies, and why not some good old standards of living. In this scenario, the exodus to Sol wouldn't be too much of a big problem, etc.
Now, I am inclined to believe the first, that is, that the GTVA's current structure is unsustainable politically given the riches and the "feel-good" politics of Sol. What is obvious here, from all our historical references, is that the powers that be were too
afraid of the explosion of unintended consequences that their scientific models were hinting at. Think about
"tipping points",
"extreme events", strange attractors diverging and all sorts of fears that were entering the minds of the psychohistorians of the GTVA. Let us consider that these minds were used to decades of a simple state of affairs where nothing particularly revolutionary was happening inside the GTVA space of politics. Let us consider as well the fearful nature of humans itself. They let their fears drive their actions.